This　article　solves　the　cooperative　adaptive　tracking　control　problem　for　nonlinear　pure-feedback　multi-agent　systems　(MASs).　Compared　with　the　previous　achievements　of　adaptive　control　of　pure-feedback　MASs,　the　partial　derivative　of　the　nonaffine　function　may　not　exist　by　using　decoupling　technology.　In　the　controller　design　framework　based　on　the　backstepping　technique,　the　additional　state　variables　are　processed　using　the　special　properties　of　the　radial　basis　function　neural　networks　(RBF　NNs).　A　special-shaped　Laplacian　matrix　is　proposed　to　unify　the　leader　gain　form　in　the　tracking　error　design　process　(the　coefficient　in　the　second　term　of　tracking　error).　Furthermore,　an　event　trigger　mechanism　(ETM)　is　introduced　to　save　resources.　The　constructed　controller　under　the　ETM　can　not　only　stabilize　the　system　states　but　also　make　the　tracking　error　reach　a　small　accuracy.　Finally,　the　simulation　results　demonstrated　the　feasibility　of　the　proposed　method.